Problem: $-7ij + 2ik - 2i + 2 = -6j - 8$ Solve for $i$.
Answer: Combine constant terms on the right. $-7ij + 2ik - 2i + {2} = -6j - {8}$ $-7ij + 2ik - 2i = -6j - {10}$ Notice that all the terms on the left-hand side of the equation have $i$ in them. $-7{i}j + 2{i}k - 2{i} = -6j - 10$ Factor out the $i$ ${i} \cdot \left( -7j + 2k - 2 \right) = -6j - 10$ Isolate the $i$ $i \cdot \left( -{7j + 2k - 2} \right) = -6j - 10$ $i = \dfrac{ -6j - 10 }{ -{7j + 2k - 2} }$ We can simplify this by multiplying the top and bottom by $-1$. $i= \dfrac{6j + 10}{7j - 2k + 2}$